Explanation for the correct answer:Simplifying the given expression:sin[3 sin^ 1(1/5)] 0ex0ex=sin[sin^ 1(3(1/5) 4(1/5)^3)]0ex0ex=sin[sin^ 1(3/5) (4/125)]0ex0ex= ...

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Rationalization Method to Remove Indeterminate Form

sin[3 sin-11/...

Question

$\sin [3 \sin^{- 1} (\frac{1}{5})] =$

$\frac{71}{125}$

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$\frac{74}{125}$

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$\frac{3}{5}$

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$\frac{1}{2}$

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Solution

The correct option is A
$\frac{71}{125}$

Explanation for the correct answer:
Simplifying the given expression:
$\sin [3 \sin^{- 1} (\frac{1}{5})] = \sin [\sin^{- 1} (3 (\frac{1}{5}) - 4 {(\frac{1}{5})}^{3})] = \sin [\sin^{- 1} (\frac{3}{5}) - (\frac{4}{125})] = \sin [\sin^{- 1} (\frac{75 - 4}{125})] = \sin [\sin^{- 1} (\frac{71}{125})] = \frac{71}{125}$
Therefore, the correct answer is option (A).

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sin3sin-115=

The correct option is A 71125Explanation for the correct answer:Simplifying the given expression:sin3sin-115=sinsin-1315-4153=sinsin-135-4125=sinsin-175-4125=sinsin-171125=71125Therefore, the correct answer is option (A).

$\sin [3 \sin^{- 1} (\frac{1}{5})] =$